A Unified Approach to Measuring Poverty and Inequality
for a poverty line denotes a larger poverty gap measure. If a distribution’s poverty deficit curve lies to the right of another distribution’s poverty deficit curve, then the former distribution is understood to have an unambiguously lower poverty gap measure, or the former distribution has lower poverty gap measures for all poverty lines. Figure 3.4 graphs the poverty deficit curves of urban Georgia for 2003 and 2006. The vertical axis reports total deficit, which is directly proportional to the poverty gap measure for the corresponding poverty line. The solid line denotes the poverty deficit curve for 2003, while the dashed line denotes the poverty deficit curve for 2006. We saw earlier that the urban poverty gap measure is higher in 2006 for both poverty lines: GEL 75.4 and GEL 45.2. What about other poverty lines? Can we say that poverty has unambiguously fallen for any poverty line? The graph suggests that we may not be able to. If we set the hypothetical poverty line to about GEL 320, then the poverty gap measure would have been lower in 2006 than in 2003. Lessons for Policy Makers Although such a poverty line seems very high and unlikely to be set at that value, the main point of the exercise is clear. When two poverty deficit curves cross, then an unambiguous judgment cannot be made based on the poverty gap measure. Given the infinite number of possible poverty lines, it would be cumbersome to check them all one by one. Instead, the poverty deficit curve is a convenient way of checking for dominance (if two poverty deficit curves never cross). If dominance does not hold, then the graph can tell us which part is responsible for the ambiguity. Poverty Severity Curve A poverty severity curve is useful when performing a dominance analysis of the squared gap measure with respect to the poverty line. In this dominance exercise, the welfare indicator is the per capita consumption expenditure, assessed by lari. In figure 3.5, the horizontal axis denotes the welfare indicator or the per capita consumption expenditure. The height of the poverty severity curve is proportional to the squared gap measure, so that a larger height for a poverty line denotes a larger squared gap. If a distribution’s poverty severity curve lies to the right of another distribution’s poverty severity curve, then the former distribution is understood to have an unambiguously
210